The present disclosure relates to systems and methods for magnetic resonance imaging (“MRI”). More particularly, the present disclosure relates to systems and methods sampling k-space with three-dimensional (3D) distributed trajectories that are non-Cartesian, such as spiral and other trajectories.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0) applied along, for example, a z axis of a Cartesian coordinate system, the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A NMR signal is emitted by the excited spins after the excitation signal B1 is terminated, this signal may be received and processed to form an image or produce a spectrum.
The MR signals acquired with an MRI system are signal samples of the subject of the examination in Fourier space, or what is often referred to in the art as “k-space”. Typically, a region to be imaged is scanned by a sequence of measurement cycles in which gradients vary according to the particular localization method being used. Each MR measurement cycle, or pulse sequence, typically samples a portion of k-space along a sampling trajectory characteristic of that pulse sequence. This is accomplished by employing magnetic fields (Gx, Gy, and Gz) that have the same direction as the polarizing field B0, but which have a gradient along the respective x, y, and z axes. By controlling the strength of these gradients during each NMR cycle, the spatial distribution of spin excitation can be controlled and the location of the resulting NMR signals can be identified. The acquisition of the NMR signals samples is referred to as sampling k-space, and a scan is completed when enough NMR cycles are performed to adequately sample k-space. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
In conventional, fully-sampled MRI, the number of acquired k-space data points is determined by the spatial resolution requirements, and the Nyquist criterion for the alias-free field of view (FOV). Images can be reconstructed, however, using a reduced number of k-space samples, or “undersampling”. The term undersampling here indicates that the Nyquist criterion is not satisfied, at least in some regions of k-space. Undersampling is used for several reasons, including reduction of acquisition time, reduction of motion artifacts, achieving higher spatial or temporal resolution, and reducing the tradeoff between spatial resolution and temporal resolution.
Most pulse sequences sample k-space in a raster scan-like pattern sometimes referred to as a “spin-warp”, a “Fourier”, a “rectilinear” or a “Cartesian” scan. The time required to fully sample 3D Cartesian k-space is relatively long. This reduces the temporal resolution of time-resolved studies that acquire the same imaging volume repeatedly. Well-known undersampling methods that are used to improve the temporal resolution of such time-resolved acquisitions often focus on sampling data at the periphery of k-space less frequently than at the center because aliasing artifacts that result from undersampling are not as severe if the violation of the Nyquist criterion is restricted to the outer part of k-space.
Alternative, non-Cartesian trajectories can also provide faster sampling of k-space, and more efficient use of the gradients. When a very fast volume acquisition is required, undersampling strategies can be used in conjunction with these non-Cartesian trajectories to further reduce the scan time.
For example, “radial”, or “projection reconstruction” scans, in which k-space is sampled as a set of radial sampling trajectories extending from the center of k-space, are often employed. The pulse sequences for a radial scan are characterized by the lack of a phase encoding gradient and the presence of a readout gradient that changes direction from one pulse sequence view to the next.
One such method that preserves reasonable image quality, while reducing the acquisition time by approximately half compared to a fully-sampled acquisition, is the so-called “vastly undersampled projection acquisition” or “VIPR” method, as described by Barger V A, Block W F, Toropov Y, Grist T M, Mistretta C A. Aliasing caused by undersampling in this method often can be tolerated in angiographic applications because the vessel-tissue contrast is high and the artifacts are distributed, or “spread” out in the image.
Another non-Cartesian, but non-radial, sampling strategy utilizes a spiral. For example, as illustrated in FIG. 1A, the sampling pattern takes the form an Archimedean spiral that, often, begins at the center of k-space and spirals out toward the periphery of k-space. The spiral sampling pattern is non-radial because the sampling trajectory does not extend primarily in a radial direction, but curves with a primary direction that, at any given point, is approximately transverse to a radial direction and only moves radially outward or inward in a secondary direction.
As illustrated in FIG. 1B, the sampling extends in a plane that can be arranged in three-dimensional space. Furthermore, as illustrated in FIG. 1C, multiple spiral trajectories can be nested within each other to more fully sample k-space, even within a single plane. When extended to a 3D sampling, the spiral trajectory can be formed into a conventional “stack of spirals” (SOS), as illustrated in FIGS. 1D and 1E. Thus, FIGS. 1A-1E show that a 2D Archimedean spiral (FIG. 1A) can be played out in 3D k-space preceded by a phase encoding gradient to position it in a desired plane of a 3D space (FIG. 1B). Several interleafs can be placed in the same plane, but rotated uniformly to nest the samples and, thereby, fully sample that plane (FIG. 1C). These planes are then repeated at many levels along the transverse axis, forming a conventional 3D “stack of spirals” trajectory to sample a cylinder (FIG. 1D. Cutting through the plane of the axes illustrates rectangular intra-trajectory sampling (FIG. 1E).
The general SOS concept can be modified to cover a sphere using stacking planes that vary in diameter from widest at the middle to small at the top and bottom. For example, FIG. 1F shows a sphere of stacked planes in this configuration. The composite spirals that make up each plane will vary, such that there will not be just one spiral that is rotated each time. This composite spiral architecture that forms each plane, with spirals that have varied diameters between planes presents a fundamental challenge in implementing this method within the clinical setting. That is, the complex and varied sampling pattern requires substantial planning of the pulse sequence and taxing operation of the gradient systems to implement in an efficient manner without undesirable scan times.
One particular implementation of a spherical sampling method is disclosed in U.S. Pat. No. 5,532,595, which utilizes a so-called “shells” k-space sampling trajectory. In this method, a spiral pattern is sampled in k-space around a spherical surface. A complete image acquisition is comprised of a series of such spiral sampling patterns over a corresponding series of spheres of increasing diameter. The shells k-space sampling trajectory acquires 3D data on concentric spherical surfaces in k-space.
Another variation or extension of the common aspects of the spiral concepts is reflected in the “stack of cones” (SOC) concept. Referring to FIG. 2A, an individual spiral can be played along a cone (starting at the center of k-space). When viewed from the vertical axis, this cone appears as a spiral and, just as described above with respect to FIG. 1, within the context of cones, multiple samplings can be nested. As illustrated in FIG. 2B, each cone is rotated about the vertical axis to fully sample a three-dimensional (3D) cone. As illustrated in FIG. 2C, multiple cones can be stacked inside each other to, thereby, sample a sphere. Like the sphere of stacked planes, the composite spirals that make up each cone will vary, such that there will not be just one cone that is rotated each time, but the cones must vary in design. This presents a fundamental challenge in implementing this method within a clinical setting.
Thus, while a number of non-Cartesian and even non-radial, 3D, sampling patters exist, each has its respective advantages and disadvantages. However, all suffer from the need to carefully plan and select imaging settings that will produce a desirable image without unacceptably long scan times. Of course, beyond careful planning of the acquisition, scan times can be reduced or at least controlled using undersampling. However, designing and implementing an undersampling strategy in conjunction with these non-Cartesian trajectories further adds complexity and extends the amount of pre-planning that is necessary, such that the requisite “homework” or pre-planning can outweigh the benefits.
Therefore, it would be desirable to have a system and method for acquiring robust sets of k-space data within a scanning duration that is clinically acceptable, but without the need for clinicians to develop extensive implementation plans to select a particular sampling methodology and balance the tradeoffs of the particular sampling methodology, such as image quality and undersampling/scan time permitted to achieve sufficient image quality for the particular clinical images desired.